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  • τ-function of discrete isomonodromy transformations and probability

  • Part of
  • D. Arinkin, A. Borodin
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 3 / May 2009
    Published online by Cambridge University Press:
    01 May 2009, pp. 747-772
    Print publication:
    May 2009
    • Article
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  • We introduce the τ-function of a difference rational connection (d-connection) and its isomonodromy transformations. We show that in a continuous limit ourτ-function agrees with the Jimbo–Miwa–Ueno τ-function. We compute the τ-function for the isomonodromy transformations leading to difference Painlevé V and difference Painlevé VI equations. We prove that the gap probability for a wide class of discrete random matrix type models can be viewed as the τ-function for an associated d-connection.